A new reduced-basis method based on the least square mapping was suggested to improve the efficiency of solving complex and multi-parameterized problems in mechanical engineering.In this method,sampling points were obtained from the parameter domain,and a reduced-basis space was constructed by computing responses of the problem at these points.Then the least square mapping was employed to conduct projection from original space onto the reduced-basis space.A reduced system was obtained and

can be solved efficiently.By projecting the reduced solution back into the original space,an approximate solution of the original system was obtained efficiently and accurately.Even with new variables, the solution can be obtained fastly by solving the reduced system.The numerical example demonstrates that this method is of validity and reliability.

reduced-basis method, least square mapping, multi-parameterized problem, Latin hypercube sampling

针对机械工程中复杂结构多参数问题,提出一种新的基于最小二乘映射的减基法。该方法通过在参数域采集样本点，计算系统在有限个样本点下的响应以构造减基空间,利用最小二乘映射把原方程向减基空间进行投影得到减缩方程，在减基空间快速求解该减缩系统，获得原问题的减缩解，并把减缩解还原到原空间，得到问题的近似解。当系统参数发生变化时，能通过减缩系统快速得到新参数下的响应，极大地提高了计算效率。最后将该方法用于赛车车架刚度计算,结果表明方法是有效且可靠的。

减基法, 最小二乘映射, 多参数问题, 拉丁超立方采样

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